Transcript TMD and Spin in SIDIS -experiments-

Transversity & friends from
HERMES
Delia Hasch
outline:
a very brief introduction
1 and 2 hadron production: transversity + Sivers fct.
theory meets experiments
International workshop on hadron and spectroscopy, Torino, Italy, 31. March – 02. April 2008
quark structure of the nucleon
q
q
unpolarised quarks
and nucleons
q

longitudinally polarised
quarks and nucleons
transversely polarised
quarks and nucleons
[also: h1q, Tq]
q: helicity-flip of both nucleon and quark
q is chiral-odd  needs a chiral odd partner:
 ep ehX    eq eq  q( x)  FF qh ( z )
q
chiral-odd fragmentation
function acts as polarimeter
of transverse quark
polarisation
chiral-odd
PDF

chiral-odd
FF
chiral-even
1hadron production: “Collins-effect”
Collins FF H1(z,kT2) correlates transverse spin of fragmenting quark
and transverse momentum Ph of produced hadron h
h
q
q
h
 left-right (azimuthal) asymmetry in the direction
of the outgoing hadron
our observable: single-spin azimuthal asymmetry
is this observable unique?
“Sivers-effect ”
another mechanism that produces single-spin azimuthal asymmetries:
Sivers distribution function : distribution of unpolarised quarks in a
transversely polarised nucleon  describes spin-orbit correlations
[Matthias Burkardt]
a non-zero Sivers fct. requires non-zero orbital angular momentum !
polarised
DISh
cross section
dσ ( x, y, z, Ph ,  ,...) 
h
dσUU  cos 2 dσUU
q(x)
UU
beam: target:

SL ,ST
1
1
 cos  dσUU  λ sin  dσ LU
Q
Q




1
1
 S L sin 2 dσUL  sin  dσUL   λ S L dσ LL  cos  dσ LL 
Q
Q




q(x)

1 
 ST sin(   S )dσUT  sin(   S )dσUT  sin( 3  S )d UT  ...
Q 


1 
  ST cos(  S )  ...  ....
Q 

polarised DISh cross section
dσ h ( x, y, z, Ph ,  ,...) 
dσUU
1
1
 cos 2 dσUU  cos  dσUU  λ sin  dσ LU
Q

 Q

q(x) h1  H1
e  H1  ...




1
1
 S L sin 2 dσUL  sin  dσUL   λ S L dσ LL  cos  dσ LL 
Q
Q




q  H1  f1T  D1  hL ...
q(x)

1 
 ST sin(   S )dσUT  sin(   S )dσUT  sin( 3  S )d UT  ...
Q 

q  H

1
transversity
(Collins effect)
f1T  D1

1 
  S cos(  S )  ...  ....
SIDIS with transversely T 
Q 

polarised targets but not only…
extraction of azimuthal amplitudes
definition of angles + asymmetries acc. to “Trento convention”
[PRD70(2004),117504]
unbinned Maximum Likelihood fit
to the log of the weighted PDF :

Fi sin(   S )
h
UT

L   ( Fi ) wi
,..., P,  , S  1 
i
P [ 2 sin(   S )
sin(   S )  2 sin(   S )
UT
 2 sin( 3  S )
sin( 3  S )  2 sin( 2  S )
UT
 2 sin( S )
h
UT
h
h
sin( S ) ]
h
UT
sin(   S )
h
UT
sin( 2  S )
fixed parameters for: cos( )
UU
…takes into account cross contamination of moments
 cos(2 )
UU
Collins asymmetries
ep  p X
p
δq( x)  H1q ( z )
first time: transversity &
Collins FF are non-zero!
• p asymmetries positive – no
surprise: u-quark dominance and
expect q>0 since q>0
• large negative p asymmetries
– ARE a surprise: suggests the
disfavoured CollinsFF being large
and with oposite sign:
p
H1,disfav ( z )   H1,fav ( z )
Collins asymmetries
ep  K X
K
δq( x)  H1q ( z )
first time: transversity &
Collins FF are non-zero!
K+ amplitudes consistent with p
amplitudes as expected from uquark dominance
K of opposite sign from p
(K is all-sea object)
more Collins asymmetries
neutral pions: important ‘control’ asymmetry (isospin)
δq( x)  H1q ( z )
holds for all tw-2 and tw-3
DF in LO and NLO in as
more Collins asymmetries
neutral pions: important ‘control’ asymmetry (isospin)
δq( x)  H1q ( z )
neutral pions:
results for the three pion charge
states are consistent with
isospin symmetry
holds for all tw-2 and tw-3
DF in LO and NLO in as
fulfilled!
extracting transversity

ep ehX
 
eq eq
 q( x)  FF
q h
( z)
q
spin-dependent
fragmentation
function
e+

e+ee-


e e  p jet
p
1
jet2 X
first glimpse of transversity
global, simultaneous fit:
q

compare to a model calculation:
cQSM
xd(x)
xu(x)
xq(x)
[Efremov,Goeke,Schweitzer PRD73(2006)]
[Anselmino et al. PRD75(2007)]
first glimpse of transversity
global, simultaneous fit:
q
compare to q:
xd(x)
xu(x)

q 
[Anselmino et al. PRD75(2007)]

first glimpse of transversity
global, simultaneous fit:
q

xu(x)
looking forward:
• include new high statistic data from
BELLE and HERMES; identified hadrons
from COMPASS
xd(x)
• awaiting proton results from COMPASS
 extending to lower x
[Anselmino et al. PRD75(2007)]
spin-orbit structure
Sivers function:
[Matthias Burkardt]
a non-zero Sivers fct. requires non-zero orbital angular momentum !
Sivers asymmetries
p
f1T q ( x)  D1q ( z )
p are subtantial and positive:
• first unambiguous evidence for
a non-zero T-odd distribution
function in DIS
• a signature for quark orbital
angular momentum !
p
Sivers asymmetries
q
1T
f
p
( x)  D ( z )
• SURPRISE:
q
1
K amplitude 2.3±0.3 times
larger than for p
 conflicts with usual
expectations based on u-quark
dominance
 suggests substantial
magnitude of the Sivers fct. for
sea quarks
p
comparison to models
excellent description of pion data
but: cannot constrain sea
[Anselmino et al. PRD72(2005)]
predictions for kaons:
kaon data suggest that sea quark contribution may be significant
 see talk from D’Alesio about choice of fragmentation functions
comparison to models
excellent description of pion data
but: cannot constrain sea
[Anselmino et al. PRD72(2005)]
predictions for kaons:
[M. Anselmino @PACSPIN07]
FF from [deFlorian, Sassot, Stratmann, arXiv:0703.242]
kaon data suggest that sea quark contribution may be significant
 see talk from D’Alesio about choice of fragmentation functions
extracting the Sivers function
A
sin( S )
UT
q
1T
f
( x)  D ( z )
q
1
usual unpolarised
fragmentation
function
ToDo:
crucial test of pQCD:
( f1T q ) DIS   ( f1T q ) DY
@FAIR (GSI)
semi-inclusive 2-hadron
production
e p ep p X



2-hadron asymmetries
   
AUT  
  
~ sin( R   S )sin(  ) δq( x) H1q ( z, M h2 )
interference fragmentation function
between pions in s-wave and p-wave
• only relative momentum of hadron pair relevant
 integration over transverse momentum of hadron pair simplifies
factorisation (collinear!) and Q2 evolution
• however cross section becomes very complicated (depends on 9! variables)
models for 2-hadron asymmetries
pythia:
2
H1 ( z, M pp
, cos  ) 
2
2
H1, sp ( z, M pp
)  cos  H1, pp ( z, M pp
)
[Jaffe et all, PRL80(1998)]
[Bacchetta, Radici PRD74(2006)]
model for H1<|q (Mhh) combined
with various models for q(x)
r0
due to r0
interference
w
r0
Mpp (GeV)
2-hadron asymmetries
q
1
δq( x) H ( z, M pp )
• BOTH: transversity and
e p  e p p  X
interference fragmention function
are non-zero !
[arXiv:0803.2367]
models for 2-hadron asymmetries
pythia:
model calculation for H1<|q (z)
combined with various models for q(x)
[Jaffe et all, PRL80(1998)]
r0
[Bacchetta, Radici PRD74(2006)]
shape compares
well
ruled out
Mpp (GeV)
2-hadron asymmetries
~ q( x) H ( z, M pp )
q
1
• first evidence for non-zero interference FF
• BELLE plans to measure it !

• this kind of interference effect is a very promising
way to access q @RHIC
q(x) from SIDIS  pp  ee-
where do we stand ?
precision of data for identified hadrons adequate for quantitative
extraction of flavour dependence of both transversity and Sivers fct
where do we stand ?
precision of data for identified hadrons adequate for quantitative
extraction of flavour dependence of both transversity and Sivers fct
more to come:
1/7/07@ 1:09:56 am
T
where do we stand ?
precision of data for identified hadrons adequate for quantitative
extraction of flavour dependence of both transversity and Sivers fct
more to come:
PT-weighted Collins and Sivers asymmetries
 model-independent interpretation of asymmetries
 requires control of acceptance effects (more @transversity08)
Boer-Mulders fct. via <cos(2)>, <kT> via Cahn-effect <cos>
 requires control of acceptance effects (more @transversity08)
<cos(S)>LT : access to tw-2 fct. g1T ; other AUT moments
T
inclusive pion photoproduction AUT (“E704 effect”)
stay tuned !
BACKUP SLIDES
[courtesy of A. Bacchetta]
Sivers asymmetries
q
1T
f
( x)  D ( z )
q
1
neutral pions:
results for the three pion
charge states are consistent
with isospin symmetry
contributions from VM
AUT of VM prod.n and decay distributions not yet available for a correction …
resolving the convolution integral
 pT weighted asymmetries:
what about the PT weighted asymmetries?
MC study of acceptance effects:
gmc_trans: generator for transversity + TMDs
Collins
asymmetries
unweighted
[L. Pappalardo, PhD Thesis University Ferrara]
what about the PT weighted asymmetries?
MC study of acceptance effects:
gmc_trans: generator for transversity + TMDs
Collins
asymmetries
weighted
[L. Pappalardo, PhD Thesis University Ferrara]
what about the PT weighted asymmetries?
acceptance depends strongly on PT:
<pT>=<kT>=0.38, constant
what about the PT weighted asymmetries?
solutions under study:
very promising  more details @transversity08, Ferrara, May 28-31
multiplicities compared to theory
new FF from combined NLO analysis of single-inclusive hadron production
in ee, pp and DIS
[deFlorian,Sassot,Stratmann arXiv:0708.0769]